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Polyanin A., Manzhirov A.V. — Handbook of Mathematics for Engineers and Scientists
Polyanin A., Manzhirov A.V. — Handbook of Mathematics for Engineers and Scientists

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Название: Handbook of Mathematics for Engineers and Scientists

Авторы: Polyanin A., Manzhirov A.V.

Аннотация:

The Handbook of Mathematics for Engineers and Scientists covers the main fields of mathematics and focuses on the methods used for obtaining solutions of various classes of mathematical equations that underlie the mathematical modeling of numerous phenomena and processes in science and technology. To accommodate different mathematical backgrounds, the preeminent authors outline the material in a simplified, schematic manner, avoiding special terminology wherever possible.

Organized in ascending order of complexity, the material is divided into two parts. The first part is a coherent survey of the most important definitions, formulas, equations, methods, and theorems. It covers arithmetic, elementary and analytic geometry, algebra, differential and integral calculus, special functions, calculus of variations, and probability theory. Numerous specific examples clarify the methods for solving problems and equations. The second part provides many in-depth mathematical tables, including those ofexact solutions of various types of equations.

This concise, comprehensive compendium of mathematical definitions, formulas, and theorems provides the foundation for exploring scientific and technological phenomena.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 600

Добавлена в каталог: 30.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$l_2$-norm      314
Abel convergence criterion functional series      349
Abel convergence criterion power series      341
Abel differential equation, first kind      462
Abel differential equation, first kind, canonical form      463
Abel differential equation, second kind      464
Abel differential equation, second kind, canonical form      465
Abel differential equations      462—465
Abel functional equation      914
Abel identity      902
Abel integral equation      1385
Abel integral equation generalized      1386
Abel integral equation, second kind      1392
Abel integral equation, second kind, generalized      1393
Abel theorem      343 411
Abel theorem, on convergence of power series      351
Abel transformation      345
Abel — Dini convergence criterion for series      341
Abel — Ruffini theorem      162
Abelian group      226
Abscissa axis      78
Abscissa of point      79 115
Absence of aftereffect      1075
Absolute convergence      342
Absolute convergence of infinite products      348
Absolute extremum      991
Absolute moment      1044
Absolute value of real number, xxx      8
Absolute value theorem      296
Absolute value theorem, double integral      318
Absolute value theorem, triple integral      325
Absolutely convergent functional series      348
Absolutely convergent infinite product      348
Absolutely convergent series      342
Acceleration of convergence of series      345
Acceleration vector      381
Acceptance region      1095
Acute triangle      43
Addition inverse hyperbolic functions      41
Addition inverse trigonometric functions      33
Addition theorem      1055
Addition, asymptotic series      364
Addition, hyperbolic functions      37
Addition, matrices      168
Addition, real numbers      6
Addition, trigonometric functions      28
Additive inverse of real number      6
Additive separable solution      571 596 597 678
Additively inverse matrix      169
Additivity of conditional expectation      1063
Adjoint matrix      170
Adjoint operator      206
Adjugate matrix      180
Adjusted sample variance      1088
Admissible controlled process      1010
Admissible element      1009
Admissible extremal      994 998
Admissible function      993 1002 1006
Affine coordinate system      190
Affine space      189
Affine space, axioms      189
Affine space, dimension      190
Affine space, point      189
Airy equation      955
Airy functions      477 955
Airy functions, first kind      955
Airy functions, second kind      955
Airy stress function      1295
Algebra      155
Algebra of sets      1032
Algebraic branch point      415
Algebraic curve      87
Algebraic curve on plane      87
Algebraic equation arbitrary degree      161
Algebraic equation binomial      161
Algebraic equation bounds for roots      163
Algebraic equation cubic      158
Algebraic equation fourth — degree      159
Algebraic equation incomplete cubic      158
Algebraic equation linear      157
Algebraic equation nth — degree      162
Algebraic equation quadratic      158
Algebraic equation reciprocal      160 161
Algebraic equation, complete cubic      159
Algebraic equation, discriminant      163
Algebraic equation, reciprocal modified      160
Algebraic equation, roots and coefficients      163
Algebraic equations      157—167
Algebraic multiplicity      209
Algebraic multiplicity, eigenvalue      184
Alternative Fourier transform      444
Alternative Fredholm      834
Alternative hypothesis      1094
Altitude, pyramid      63
Altitude, trapezoid      54
Altitude, triangle      46
Amplitude      973
Analogs Neper      73
Analysis sequential      1097
Analysis variance      1107
Analytic continuation      418
Analytic function      413
Analytic geometry      77
Angle between coordinate axes and segments      82
Angle between elements      193
Angle between lines in space      135
Angle between planes      137
Angle between straight line and plane      139
Angle between two straight lines      94
Angle between vectors      120
Angle bisector of triangle      45 46
Angle central      55 56
Angle dihedral      60
Angle edge      60
Angle external      43
Angle inscribed      56
Angle interior      43
Angle interior of polygon      51
Angle polar      80
Angle polyhedral      60 61
Angle solid      61
Angle trihedral      60
Angle trisectors      49
Angle, face      60
Angles in space      59
Angles symmetric polyhedral      61
Angular point      252
Annihilating polynomial      186
Annulus      58
Antagonistic game      1024
Antagonistic two-person zero-sum game      1024
Antagonistic two-person zero-sum game, minimax theorem      1026
Antiderivative      273
Antihermitian matrix      168
Antiperiodic functions      885
Antisymmetric matrix      168
Apex      67
Apex of pyramid      63
Apothem of regular pyramid      64
Appell transformation      1268
Applicable surfaces      395
Applicate of point      115
Approximation function      508
Approximation, best mean-square      1063 1066
Arbitrary curvilinear coordinate systems      1195
Arbitrary series      341
Arc geodesic      70
Arc length      390
Arc length differential      390
Arc regular      379
Arccosine, xxx      32
Arccotangent, xxx      32
Arcsine, xxx      31
Arctangent, xxx      32
Area polygon      83
Area triangle      83
Argument      236
Argument increment      992
Argument, complex number      400
Argument, variation      992
Arithmetic      3
Arithmetic mean      13
Arithmetic mean of functions      297
Arithmetic progression      11
Arithmetic root      8
Arithmetic sequence      11
Arithmetic series      11
Arm of hyperbola      101
Arrangement      1033
Arrangement with repetitions      1034
Artificial basic variables      1016
Ascending Landen transformation      975
Associated Legendre functions      964 965
Associated Legendre functions, first kind      965
Associated Legendre functions, second kind      965
Associated linear space of affine space      189
Associated vector      213
Associative composition law      225
Asymmetric form of Fourier cosine transform      445
Asymmetric form of Fourier sine transform      446
Asymmetric form of Fourier transform      444
Asymmetry coefficient      1045
Asymptote      241 374
Asymptote oblique      242
Asymptote vertical      242
Asymptotes      241 374
Asymptotes of hyperbola      101
Asymptotic cone      144
Asymptotic expansion      363
Asymptotic formulas, calculation of integrals      290
Asymptotic formulas, improper integrals with parameter      307
Asymptotic formulas, Laplace integrals of general form      292
Asymptotic formulas, Laplace integrals of special form      291
Asymptotic formulas, power Laplace integral      294
Asymptotic lines      393
Asymptotic point      373
Asymptotic properties of Fourier coefficients      359
Asymptotic series      363
Asymptotic series integration      365
Asymptotic series, addition      364
Asymptotic series, division      364
Asymptotic series, multiplication      364
Asymptotic series, Poincare type      363
Asymptotic series, subtraction      364
Asymptotic stability      546 549
Asymptotic zero      364
Asymptotically stable solution      546
Asymptotically unbiased estimator      1089
Attractive fixed point      908
Augmented matrix      198
Auto — Backlund transformations      663
Autocorrelation function      1072
Automorphic function      912
Automorphism of group      227
Autonomous equation      525 1207 1223 1225
Autonomous system, equilibrium point      545
Autonomous system, general form      1240
Autonomous system, ODEs      545
Averaging method      503
Axioms of affine space      189
Axis      77
Axis, coordinate of point      77
Axis, coordinate system      77
Axis, imaginary      401
Axis, imaginary of hyperbola      101
Axis, iteration      876
Axis, ordinate      78
Axis, polar      80
Axis, principal      152
Axis, principal of hyperbola      101
Axis, principal of second-order curve      109
Axis, real      235
Axis, semiminor of ellipse      98
Axisymmetric steady hydrodynamic boundary layer      712
Babbage equation      917 1416 1423
Backlund transformation      497 663—665
Backward Kolmogorov equation      1076
Backward substitution in Gaussian elimination method      200
Balanced transportation problem      1020
Ball      68
Banach problem      1038
Banach space      196
Bartlett test      1103
Base face of prism      61
Base, cylinder      65
Base, isosceles triangle      50
Base, natural (Napierian) logarithms      9 22 23
Base, pyramid      63
Base, spherical segment      69
Base, trapezoid      54
Basic columns      178
Basic equation of information theory      1440
Basic inequalities for mean values      13
Basic integrals      274
Basic matrix of linear system of algebraic equations      197
Basic minor      177 178
Basic properties inequalities      5
Basic properties, equalities      5
Basic rows      178
Basic variable      1015
Basic variable artificial      1016
Basis canonical      217
Basis linear space      189
Basis orthonormal      194
Bayes formula      1036 1063
Bellman equations      1028
Bellman optimality principle      1028
Bending      395
Bernoulli equation      458 1207
Bernoulli formula      1037
Bernoulli numbers      938
Bernoulli polynomials      891 988
Bernoulli process      1037
Bernoulli scheme      1037
Bernoulli theorem      1070
Bertrand convergence criterion for series      340
Bessel equation      1216
Bessel equation, modified      1216
Bessel formula      950
Bessel function      947 1216
Bessel function, first kind, xxxi      947 1216
Bessel function, second kind, xxxii      947 1216
Bessel function, third kind      952
Best mean-square approximation      1063 1066
beta function      945
Biangles, spherical      71
Biased estimator      1089
Bicylindrical coordinates      1204
Biharmonic equation      1297
Bilinear form      214 992
Bilinear form, degenerate      215
Bilinear form, Euclidean space      219
Bilinear form, finite-dimensional space      215
Bilinear form, matrix      215
Bilinear form, nondegenerate      215
Bilinear form, polar      216
Bilinear form, rank      215
Bilinear form, skew-symmetric      214
Bilinear form, symmetric      214
Bilinear functional      992
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